f[t_,y_]:=4 - t + 2*y;
dfield=VectorPlot[{1, f[t,y]},{t, 0,5},{y,-3,3},Axes->True,VectorScale->{Tiny,Automatic,None},AxesLabel->{"t","dydt=4-t+2y"}]

sol1=DSolve[{y'[t]== f[t, y[t]],y[0]==-7/4},y[t],t];
sol2=DSolve[{y'[t]== f[t, y[t]],y[0]==-7/4-1/1024},y[t],t];
sol3=DSolve[{y'[t]== f[t, y[t]],y[0]==-7/4+1/1024},y[t],t];
pp1=Plot[y[t]/.sol1,{t,0,5}];
pp2=Plot[y[t]/.sol2,{t,0,5}];
pp3=Plot[y[t]/.sol3,{t,0,5}];
Show[dfield,pp1,pp2, pp3]

f[t_,y_]:=4 *t - 2*y/t;
dfield=VectorPlot[{1, f[t,y]},{t, -2,2},{y,-1.5,3.5},Axes->True,VectorScale->{Tiny,Automatic,None},AxesLabel->{"t","dydt=4t-2y/t"}]

sol1=DSolve[{y'[t]== f[t, y[t]],y[1]==1.5},y[t],t];
sol2=DSolve[{y'[t]== f[t, y[t]],y[1]==1},y[t],t];
sol3=DSolve[{y'[t]== f[t, y[t]],y[1]==.5},y[t],t];
pp1=Plot[y[t]/.sol1,{t,0,2}];
pp2=Plot[y[t]/.sol2,{t,-2,2}];
pp3=Plot[y[t]/.sol3,{t,0,2}];
Show[dfield,pp1,pp2, pp3]